Mignolet had been expected to be shipped out of Anfield having fallen down to third in the goalkeeping pecking order behind new arrival Alisson Becker and Karius, whose mistakes in the Champions League final proved to be the beginning of the end for him at Liverpool.
However, Karius was instead sent on a two-year loan to Besiktas which is expected to become permanent, prompting Mignolet to describe Liverpool's decision as "bizarre".
"Discussing your individual problems in public doesn't make too much sense," Klopp told reporters at his pre-match press conference.
"It was still okay. If he was happy to be a number two then I wouldn't know him - he's a top professional.
"If you want to say something, say it to me directly than to a newspaper. He's on pretty good pay at Liverpool by the way."
Alisson is yet to concede a goal during his three competitive outings for Liverpool.